The computation of \(W_n\)  is as written in (REF ). As
mentioned above, we evaluate \(W_n\)  under a known standard deviation
\(\sigma _\varepsilon \)  of the error distribution. The
optimization step in (REF ) is computed using a
combination of a global and local search. A uniformly random point in drawn in
\(\mathbb {R}^{K_n}\)  and this serves as the initial point in the constrained nonlinear global
optimizer ISRES
We set a relative error tolerance of \(10^{-4}\)  and a maximum of 100 runs.
of [1]}. To further refine the solution, we take the
resulting solution point and set that as the initial point in the constrained
nonlinear local optimizer COBYLA
Again, we set a relative error tolerance of \(10^{-4}\)  and a maximum of 100 runs.
of [2]}. The end of this procedure results in our small-uniform statistic \(W_n\) .
Although not thoroughly experimented in this paper, but we sense the specific
choices of these numerical optimization algorithms are not particularly important.
